If your web games use plugins it might be related to known problems in the Labs build
You'll experience choppy scrolling on pages with embedded Flash
Scrolling inside windowed Flash is not working
WMP player plugin controls get corrupted after scrolling
Silverlight may have some issues
Opera may crash on resizing the plugin window
Minimal restart in Opera's crashlog dialog works as a full restart
You'll experience a temporary freeze when deleting plugin data
Some strings in 64bit Opera will suffer corrupted text substitutions
The Shockwave Director plugin is not detected under 64bit Opera
You could try setting History Navigation Mode to 3 in opera:config it uses the cache when going back or forwards in a tabs history pages are loaded instantly , not sure if it will help your problem but it's well worth doing especially on a slow connection.
Open opera:config & search for history look in the User Prefs section , set History Navigation Mode to 3 & make sure you save.